Worksheets12 General Unit 3 Topic 1 (2) 2020
Total questions: 17
Worksheet time: 51mins
When using a least squares regression line to model a relationship displayed in a scatterplot, one key assumption is that:
there are two variables
the variables are related
the variables are linearly related
r2 > 0.5
the correlation coefficient is positive
In the least squares regression line y = −1.2 + 0.52x:
the y-intercept = −0.52 and slope = −1.2
the y-intercept = 0 and slope = −1.2
the y-intercept = 0.52 and slope = −1.2
the y-intercept = −1.2 and slope = 0.52
the y-intercept = 1.2 and slope = −0.52
If the equation of a least squares regression line is
y = 8 − 9x and R2 = 0.25:
r = −0.5
r = −0.25
r = −0.0625
r = 0.25
r = 0.50
The least squares regression line y = 8 − 9x predicts that, when x = 5, the value of y is:
−45
−37
37
45
53
A least squares regression line of the form
y = a + bx is fitted to the data set shown.
The equation of the line is:
y = −0.69 + 24.4x
y = 24.4 − 0.69x
C y = 24.4 + 0.69x
y = 28.7 − x
y = 28.7 + x
A least squares regression line of the form y = a + bx is fitted to the data set shown.
The equation of the line is:
y = 1 + 0.5x
y = 0.5 + x
y = 0.5 + 7.5x
y = 7.5 + 0.5x
y = 30 − 0.5x
Given that r = 0.733, sx = 1.871 and sy = 3.391, the slope of the least squares regression line is closest to:
0.41
0.45
1.33
1.87
2.49
Using a least squares regression line, the predicted value of a data point is 78.6. The residual value is –5.4. The actual data value is:
73.2
84.0
88.6
94.6
424.4
The equation of the least squares regression line plotted on the scatterplot opposite is closest to:
y = 8.7 − 0.9x
y = 8.7 + 0.9x
y = 0.9 − 8.7x
y = 0.9 + 8.7x
y = 8.7 − 0.1x
The equation of the least squares regression line
plotted on the scatterplot opposite is closest to:
y = −14 + 0.8x
y = 0.8 + 14x
y = 2.5 + 0.8x
y = 14 − 0.8x
y = 17 + 1.2x
Weight (in kg) can be predicted from height (in cm) using the regression line:
weight = −96 + 0.95 × height, with r = 0.79
Which of the following statements relating to the regression line is false?
The slope of the regression line is 0.95.
The explanatory variable in the regression equation is height.
The least squares line does not pass through the origin.
The intercept is 96.
he equation predicts that a person who is 180 cm tall will weigh 75 kg.
Weight (in kg) can be predicted from height (in cm) using the regression line:
weight = −96 + 0.95 × height, with r = 0.79
This regression line predicts that, on average, weight:
decreases by 96 kg for each 1 centimetre increase in height
increases by 96 kg for each 1 centimetre increase in height
decreases by 0.79 kg for each 1 centimetre increase in height
decreases by 0.95 kg for each 1 centimetre increase in height
increases by 0.95 kg for each 1 centimetre increase in height
Weight (in kg) can be predicted from height (in cm) using the regression line:
weight = −96 + 0.95 × height, with r = 0.79
Noting that the value of the correlation coefficient is r = 0.79, we can say that:
62% of the variation in weight can be explained by the variation in height
79% of the variation in weight can be explained by the variation in height
88% of the variation in weight can be explained by the variation in height
79% of the variation in height can be explained by the variation in weight
95% of the variation in height can be explained by the variation in weight
Weight (in kg) can be predicted from height (in cm) using the regression line:
weight = −96 + 0.95 × height, with r = 0.79
A person of height 179 cm weighs 82 kg. If the regression equation is used to predict their weight, then the residual will be closest to:
-8 kg
3 kg
-3 kg
9 kg
74 kg
The coefficient of determination for the
data displayed in the scatterplot opposite
is close to R2 = 0.5. The correlation coefficient is closest to:
-0.7
-0.25
0.25
0.5
0.7
There is a strong, linear, positive correlation (r = 0.85) between the amount of garbage recycled and salary level.
From this information, we can conclude that:
the amount of garbage recycled can be increased by increasing people’s salaries
the amount of garbage recycled can be increased by decreasing people’s salaries
increasing the amount of garbage you recycle will increase your salary
people on high salaries tend to recycle less garbage
people on high salaries tend to recycle more garbage
There is a strong, linear, positive correlation (r = 0.95) between the marriage rate in Kentucky and the number of people who drown falling out of a fishing boat.
From this information, the most likely conclusion we can draw is:
reducing the number of marriages in Kentucky will decrease the number of people who drown falling out of a fishing boat
increasing the number of marriages in Kentucky will increase the number of people who drown falling out of a fishing boat
this correlation is just coincidence, and a change in the marriage rate will not affect the number of people drowning in Kentucky in any way
only married people in Kentucky drown falling out of a fishing boat
stopping people from going fishing will reduce the marriage rate in Kentucky
